We perform discrete element simulations of freely cooling, dense granular materials, previously sheared at a constant rate. Particles are identical, frictional spheres interacting via linear springs and dashpots and the solid volume fraction is constant and equal to 60% during both shearing and cooling. We measure the average and the distributions of contacts per particle and the anisotropy of the contact network. We observe that the granular material, at the beginning of cooling, can be shear-jammed, fragile or unjammed. The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively. While anisotropic solids and isotropic fluids rapidly reach an apparent final steady configuration, the microstructure continues to evolve for anisotropic fluids. We explain this with the presence of vortices in the flow field that counteract the randomizing and structure-annihilating effect of collisions. We notice, in accordance with previous findings, that the initial fraction of mechanically stable particles permits to distinguish between shear-jammed, fragile or unjammed states and, therefore, determine beforehand the fate of the freely evolving granular materials. We also find that the fraction of mechanically stable particles is in a one-to-one relation with the average number of contacts per particle. The latter is, therefore, a variable that must be incorporated in continuum models of granular materials, even in the case of unjammed states, where it was widely accepted that the solid volume fraction was sufficient to describe the geometry of the system.

我们对自由冷却的致密颗粒材料进行离散元素模拟，这些材料以前以恒定的速度剪切。颗粒是相同的，摩擦球通过线性弹簧和减震器相互作用，在剪切和冷却过程中，固体体积分数恒定且等于60％。我们测量每个粒子接触的平均数和分布以及接触网络的各向异性。我们观察到，在冷却开始时，粒状材料可能会发生剪切堵塞，易碎或未堵塞。初始状态确定了致密组件随后分别演化为各向异性固体，各向同性或各向异性流体的过程。当各向异性固体和各向同性流体迅速达到表观的最终稳定构型时，各向异性流体的微观结构仍在不断发展。我们用流场中存在的涡旋来解释这一点，该涡旋抵消了碰撞的随机化和结构an灭效应。根据先前的发现，我们注意到机械稳定颗粒的初始部分可以区分受剪切干扰，易碎或不受干扰的状态，因此，可以预先确定自由发展的颗粒状材料的命运。我们还发现，机械稳定颗粒的比例与每个颗粒的平均接触数呈一一对应关系。因此，后者是一个变量，必须将其纳入粒状材料的连续模型中，即使在无堵塞状态下也是如此，在该状态下，人们普遍认为固体体积分数足以描述系统的几何形状。